%   ORIGINAL: h4/int__bitwise/int__not0
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/COND__RATOR: !x g f b. h4/bool/COND b f g x = h4/bool/COND b (f x) (g x)
% Assm: h4/bool/COND__RAND: !y x f b. f (h4/bool/COND b x y) = h4/bool/COND b (f x) (f y)
% Assm: h4/bool/COND__EXPAND: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm: h4/bool/LET__CONG: !g f N M. M = N /\ (!x. x = N ==> f x = g x) ==> h4/bool/LET f M = h4/bool/LET g N
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/marker/AC__DEF: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% Assm: h4/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/NOT__LESS__0: !n. ~h4/prim__rec/_3C n h4/num/0
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/arithmetic/MULT__ASSOC: !p n m. h4/arithmetic/_2A m (h4/arithmetic/_2A n p) = h4/arithmetic/_2A (h4/arithmetic/_2A m n) p
% Assm: h4/arithmetic/LESS__MONO__ADD__EQ: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2B m p) (h4/arithmetic/_2B n p) <=> h4/prim__rec/_3C m n
% Assm: h4/arithmetic/EQ__MONO__ADD__EQ: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/COMPLETE__INDUCTION: !P. (!n. (!m. h4/prim__rec/_3C m n ==> P m) ==> P n) ==> (!n. P n)
% Assm: h4/arithmetic/ODD__EVEN: !n. h4/arithmetic/ODD n <=> ~h4/arithmetic/EVEN n
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/LT__MULT__CANCEL__LBARE_c0: !n m. h4/prim__rec/_3C m (h4/arithmetic/_2A m n) <=> h4/prim__rec/_3C h4/num/0 m /\ h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/DIVISION: !n. h4/prim__rec/_3C h4/num/0 n ==> (!k. k = h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/DIV k n) n) (h4/arithmetic/MOD k n) /\ h4/prim__rec/_3C (h4/arithmetic/MOD k n) n)
% Assm: h4/arithmetic/DIV__UNIQUE: !q n k. (?r. k = h4/arithmetic/_2B (h4/arithmetic/_2A q n) r /\ h4/prim__rec/_3C r n) ==> h4/arithmetic/DIV k n = q
% Assm: h4/arithmetic/DIV__LESS: !n d. h4/prim__rec/_3C h4/num/0 n /\ h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) d ==> h4/prim__rec/_3C (h4/arithmetic/DIV n d) n
% Assm: h4/arithmetic/MOD__LESS: !n m. h4/prim__rec/_3C h4/num/0 n ==> h4/prim__rec/_3C (h4/arithmetic/MOD m n) n
% Assm: h4/arithmetic/DIV__LT__X: !z y x. h4/prim__rec/_3C h4/num/0 z ==> (h4/prim__rec/_3C (h4/arithmetic/DIV y z) x <=> h4/prim__rec/_3C y (h4/arithmetic/_2A x z))
% Assm: h4/arithmetic/EVEN__MOD2: !x. h4/arithmetic/EVEN x <=> h4/arithmetic/MOD x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/num/0
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c3: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/numeral__lte_c0: !n. h4/arithmetic/_3C_3D h4/arithmetic/ZERO n <=> T
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lte_c3: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/arithmetic/_3C_3D n m
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/enumeral__mult_c2: !y x. h4/arithmetic/_2A (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y) = h4/numeral/internal__mult (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y)
% Assm: h4/numeral/internal__mult__characterisation_c0: !n. h4/numeral/internal__mult h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm: h4/numeral/internal__mult__characterisation_c2: !n m. h4/numeral/internal__mult (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/numeral/internal__mult n m)) m)
% Assm: h4/basicSize/bool__size__def: !b. h4/basicSize/bool__size b = h4/num/0
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/list/list__size__def_c0: !f. h4/list/list__size f h4/list/NIL = h4/num/0
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/list/MAP__ID_c0: !l. h4/list/MAP (\x. x) l = l
% Assm: h4/list/MAP__MAP__o: !l g f. h4/list/MAP f (h4/list/MAP g l) = h4/list/MAP (h4/combin/o f g) l
% Assm: h4/list/MEM_c0: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm: h4/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__ADD__ASSOC: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm: h4/integer/int__sub0: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/INT__ADD__RID: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/integer/INT__ADD__RINV: !x. h4/integer/int__add x (h4/integer/int__neg x) = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__MUL__LID: !x. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/integer/INT__RDISTRIB: !z y x. h4/integer/int__mul (h4/integer/int__add x y) z = h4/integer/int__add (h4/integer/int__mul x z) (h4/integer/int__mul y z)
% Assm: h4/integer/INT__NEG__ADD: !y x. h4/integer/int__neg (h4/integer/int__add x y) = h4/integer/int__add (h4/integer/int__neg x) (h4/integer/int__neg y)
% Assm: h4/integer/INT__MUL__LZERO: !x. h4/integer/int__mul (h4/integer/int__of__num h4/num/0) x = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__NEG__LMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm: h4/integer/INT__NEGNEG: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integer/INT__NOT__LT: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm: h4/integer/INT__LT__GT: !y x. h4/integer/int__lt x y ==> ~h4/integer/int__lt y x
% Assm: h4/integer/INT__LE__REFL: !x. h4/integer/int__le x x
% Assm: h4/integer/INT__NEG__LT0: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm: h4/integer/INT__LT__ADD2: !z y x w. h4/integer/int__lt w x /\ h4/integer/int__lt y z ==> h4/integer/int__lt (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm: h4/integer/INT__NEG__MINUS1: !x. h4/integer/int__neg x = h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x
% Assm: h4/integer/INT__LT__IMP__NE: !y x. h4/integer/int__lt x y ==> ~(x = y)
% Assm: h4/integer/INT__LT__SUB__RADD: !z y x. h4/integer/int__lt (h4/integer/int__sub x y) z <=> h4/integer/int__lt x (h4/integer/int__add z y)
% Assm: h4/integer/INT__LT__SUB__LADD: !z y x. h4/integer/int__lt x (h4/integer/int__sub y z) <=> h4/integer/int__lt (h4/integer/int__add x z) y
% Assm: h4/integer/INT__LE__SUB__RADD: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm: h4/integer/INT__SUB__LZERO: !x. h4/integer/int__sub (h4/integer/int__of__num h4/num/0) x = h4/integer/int__neg x
% Assm: h4/integer/INT__EQ__SUB__LADD: !z y x. x = h4/integer/int__sub y z <=> h4/integer/int__add x z = y
% Assm: h4/integer/NUM__OF__INT: !n. h4/integer/Num (h4/integer/int__of__num n) = n
% Assm: h4/integer/INT__OF__NUM: !i. h4/integer/int__of__num (h4/integer/Num i) = i <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) i
% Assm: h4/integer/INT__DIVIDES__1_c0: !x. h4/integer/int__divides (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x
% Assm: h4/integer/INT__MIN__LT: !z y x. h4/integer/int__lt x (h4/integer/int__min y z) ==> h4/integer/int__lt x y /\ h4/integer/int__lt x z
% Assm: h4/integer/INT__MAX__LT: !z y x. h4/integer/int__lt (h4/integer/int__max x y) z ==> h4/integer/int__lt x z /\ h4/integer/int__lt y z
% Assm: h4/integer/INT__ADD__REDUCE_c0: !p. h4/integer/int__add (h4/integer/int__of__num h4/num/0) p = p
% Assm: h4/integer/INT__ADD__REDUCE_c1: !p. h4/integer/int__add p (h4/integer/int__of__num h4/num/0) = p
% Assm: h4/integer/INT__ADD__REDUCE_c2: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__ADD__REDUCE_c5: !n m. h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))))
% Assm: h4/integer/INT__ADD__REDUCE_c6: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))))
% Assm: h4/integer/INT__ADD__REDUCE_c7: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))))
% Assm: h4/integer/INT__SUB__CALCULATE: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/INT__SUB__REDUCE_c2: !n m. h4/integer/int__sub (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)))
% Assm: h4/integer/INT__MUL__REDUCE_c2: !n m. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2A m n))
% Assm: h4/integer/INT__MUL__REDUCE_c3: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2A m n)))
% Assm: h4/integer/INT__LT__REDUCE_c0: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c2: h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num h4/num/0) <=> F
% Assm: h4/integer/INT__LT__REDUCE_c5: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c6: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c11: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> h4/prim__rec/_3C m n
% Assm: h4/integer/INT__EQ__REDUCE_c1: !n. h4/integer/int__of__num h4/num/0 = h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) <=> F
% Assm: h4/int__arith/lt__move__left__left: !z y x. h4/integer/int__lt x (h4/integer/int__add y z) <=> h4/integer/int__lt (h4/integer/int__add x (h4/integer/int__neg y)) z
% Assm: h4/int__arith/lt__move__left__right: !z y x. h4/integer/int__lt (h4/integer/int__add x y) z <=> h4/integer/int__lt y (h4/integer/int__add z (h4/integer/int__neg x))
% Assm: h4/int__arith/eq__move__left__left: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add x (h4/integer/int__neg y) = z
% Assm: h4/int__arith/eq__move__left__right: !z y x. h4/integer/int__add x y = z <=> y = h4/integer/int__add z (h4/integer/int__neg x)
% Assm: h4/int__arith/lcm__eliminate: !c P. (?x. P (h4/integer/int__mul c x)) <=> (?x. P x /\ h4/integer/int__divides c x)
% Assm: h4/int__arith/can__get__small: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt (h4/integer/int__sub y (h4/integer/int__mul c d)) x)
% Assm: h4/int__arith/can__get__big: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__mul c d)))
% Assm: h4/int__arith/restricted__quantification__simp: !x low high. h4/integer/int__lt low x /\ h4/integer/int__le x high <=> h4/integer/int__lt low high /\ (x = high \/ h4/integer/int__lt low x /\ h4/integer/int__le x (h4/integer/int__sub high (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/int__arith/top__and__lessers: !x0 d P. (!x. P x ==> P (h4/integer/int__sub x d)) /\ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> P (h4/integer/int__sub x0 (h4/integer/int__mul c d)))
% Assm: h4/int__arith/bot__and__greaters: !x0 d P. (!x. P x ==> P (h4/integer/int__add x d)) /\ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> P (h4/integer/int__add x0 (h4/integer/int__mul c d)))
% Assm: h4/int__arith/in__additive__range: !x low d. h4/integer/int__lt low x /\ h4/integer/int__le x (h4/integer/int__add low d) <=> (?j. x = h4/integer/int__add low j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm: h4/int__arith/in__subtractive__range: !x high d. h4/integer/int__le (h4/integer/int__sub high d) x /\ h4/integer/int__lt x high <=> (?j. x = h4/integer/int__sub high j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm: h4/int__arith/subtract__to__small: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__sub x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__sub x (h4/integer/int__mul k d)) d)
% Assm: h4/int__arith/add__to__great: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__add x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul k d)) d)
% Assm: h4/int__arith/INT__NUM__FORALL: !P. (!n. P (h4/integer/int__of__num n)) <=> (!x. h4/integer/int__le (h4/integer/int__of__num h4/num/0) x ==> P x)
% Assm: h4/int__bitwise/int__not__def: !i. h4/int__bitwise/int__not i = h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/int__bitwise/bits__of__num__primitive__def: h4/int__bitwise/bits__of__num = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!n. ~(n = h4/num/0) ==> R (h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) n))) (\bits__of__num n. h4/combin/I (h4/bool/COND (n = h4/num/0) h4/list/NIL (h4/list/CONS (h4/arithmetic/ODD n) (bits__of__num (h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))
% Assm: h4/int__bitwise/bits__of__num__def: !n. h4/int__bitwise/bits__of__num n = h4/bool/COND (n = h4/num/0) h4/list/NIL (h4/list/CONS (h4/arithmetic/ODD n) (h4/int__bitwise/bits__of__num (h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))
% Assm: h4/int__bitwise/bits__of__int__def: !i. h4/int__bitwise/bits__of__int i = h4/bool/COND (h4/integer/int__lt i (h4/integer/int__of__num h4/num/0)) (h4/pair/_2C (h4/list/MAP $not (h4/int__bitwise/bits__of__num (h4/integer/Num (h4/int__bitwise/int__not i)))) T) (h4/pair/_2C (h4/int__bitwise/bits__of__num (h4/integer/Num i)) F)
% Assm: h4/int__bitwise/num__of__bits__primitive__def: h4/int__bitwise/num__of__bits = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!bs. R bs (h4/list/CONS F bs)) /\ (!bs. R bs (h4/list/CONS T bs)))) (\num__of__bits a. h4/list/list__CASE a (h4/combin/I h4/num/0) (\v bs. h4/bool/COND v (h4/combin/I (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (num__of__bits bs)))) (h4/combin/I (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (num__of__bits bs)))))
% Assm: h4/int__bitwise/int__of__bits__def: !rest bs. h4/int__bitwise/int__of__bits (h4/pair/_2C bs rest) = h4/bool/COND rest (h4/int__bitwise/int__not (h4/integer/int__of__num (h4/int__bitwise/num__of__bits (h4/list/MAP $not bs)))) (h4/integer/int__of__num (h4/int__bitwise/num__of__bits bs))
% Assm: h4/int__bitwise/bits__bitwise__tupled__primitive__def: h4/int__bitwise/bits__bitwise__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b2 r2 bs2 r1 f. R (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C h4/list/NIL r1) (h4/pair/_2C bs2 r2))) (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C h4/list/NIL r1) (h4/pair/_2C (h4/list/CONS b2 bs2) r2)))) /\ (!b1 r2 r1 bs1 f. R (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1 r1) (h4/pair/_2C h4/list/NIL r2))) (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C (h4/list/CONS b1 bs1) r1) (h4/pair/_2C h4/list/NIL r2)))) /\ (!b2 b1 r2 bs2 r1 bs1 f. R (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1 r1) (h4/pair/_2C bs2 r2))) (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C (h4/list/CONS b1 bs1) r1) (h4/pair/_2C (h4/list/CONS b2 bs2) r2)))))) (\bits__bitwise__tupled a. h4/pair/pair__CASE a (\f v1. h4/pair/pair__CASE v1 (\v2 v3. h4/pair/pair__CASE v2 (\v4 r1. h4/pair/pair__CASE v3 (\v6 r2. h4/list/list__CASE v6 (h4/list/list__CASE v4 (h4/combin/I (h4/pair/_2C h4/list/NIL (f r1 r2))) (\b1 bs1. h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\bs r. h4/pair/_2C (h4/list/CONS (f b1 r2) bs) r)) (bits__bitwise__tupled (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1 r1) (h4/pair/_2C h4/list/NIL r2))))))) (\b2 bs2. h4/list/list__CASE v4 (h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\bs r. h4/pair/_2C (h4/list/CONS (f r1 b2) bs) r)) (bits__bitwise__tupled (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C h4/list/NIL r1) (h4/pair/_2C bs2 r2)))))) (\b1_27 bs1_27. h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\bs r. h4/pair/_2C (h4/list/CONS (f b1_27 b2) bs) r)) (bits__bitwise__tupled (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1_27 r1) (h4/pair/_2C bs2 r2))))))))))))
% Assm: h4/int__bitwise/bits__bitwise__curried__def: !x2 x1 x. h4/int__bitwise/bits__bitwise x x1 x2 = h4/int__bitwise/bits__bitwise__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/int__bitwise/int__bitwise__def: !j i f. h4/int__bitwise/int__bitwise f i j = h4/int__bitwise/int__of__bits (h4/int__bitwise/bits__bitwise f (h4/int__bitwise/bits__of__int i) (h4/int__bitwise/bits__of__int j))
% Goal: h4/int__bitwise/int__not = h4/int__bitwise/int__bitwise (\x y. ~y) (h4/integer/int__of__num h4/num/0)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_CONDu_u_RATOR]: !x g f b. happ (h4/bool/COND b f g) x = h4/bool/COND b (happ f x) (happ g x)
% Assm [h4s_bools_CONDu_u_RAND]: !y x f b. happ f (h4/bool/COND b x y) = h4/bool/COND b (happ f x) (happ f y)
% Assm [h4s_bools_CONDu_u_EXPAND]: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm [h4s_bools_LETu_u_CONG]: !g f N M. M = N /\ (!x. x = N ==> happ f x = happ g x) ==> h4/bool/LET f M = h4/bool/LET g N
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_markers_ACu_u_DEF]: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% Assm [h4s_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_combins_Ku_u_THM]: !y x. h4/combin/K x y = x
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_NOTu_u_LESSu_u_0]: !n. ~happ (happ h4/prim__rec/_3C n) h4/num/0
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_MULTu_u_COMM]: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm [h4s_arithmetics_MULTu_u_ASSOC]: !p n m. h4/arithmetic/_2A m (h4/arithmetic/_2A n p) = h4/arithmetic/_2A (h4/arithmetic/_2A m n) p
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ]: !p n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/_2B m p)) (h4/arithmetic/_2B n p) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ]: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_COMPLETEu_u_INDUCTION]: !P. (!n. (!m. happ (happ h4/prim__rec/_3C m) n ==> happ P m) ==> happ P n) ==> (!n. happ P n)
% Assm [h4s_arithmetics_ODDu_u_EVEN]: !n. h4/arithmetic/ODD n <=> ~h4/arithmetic/EVEN n
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_LTu_u_MULTu_u_CANCELu_u_LBAREu_c0]: !n m. happ (happ h4/prim__rec/_3C m) (h4/arithmetic/_2A m n) <=> happ (happ h4/prim__rec/_3C h4/num/0) m /\ happ (happ h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) n
% Assm [h4s_arithmetics_DIVISION]: !n. happ (happ h4/prim__rec/_3C h4/num/0) n ==> (!k. k = h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/DIV k n) n) (h4/arithmetic/MOD k n) /\ happ (happ h4/prim__rec/_3C (h4/arithmetic/MOD k n)) n)
% Assm [h4s_arithmetics_DIVu_u_UNIQUE]: !q n k. (?r. k = h4/arithmetic/_2B (h4/arithmetic/_2A q n) r /\ happ (happ h4/prim__rec/_3C r) n) ==> h4/arithmetic/DIV k n = q
% Assm [h4s_arithmetics_DIVu_u_LESS]: !n d. happ (happ h4/prim__rec/_3C h4/num/0) n /\ happ (happ h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) d ==> happ (happ h4/prim__rec/_3C (h4/arithmetic/DIV n d)) n
% Assm [h4s_arithmetics_MODu_u_LESS]: !n m. happ (happ h4/prim__rec/_3C h4/num/0) n ==> happ (happ h4/prim__rec/_3C (h4/arithmetic/MOD m n)) n
% Assm [h4s_arithmetics_DIVu_u_LTu_u_X]: !z y x. happ (happ h4/prim__rec/_3C h4/num/0) z ==> (happ (happ h4/prim__rec/_3C (h4/arithmetic/DIV y z)) x <=> happ (happ h4/prim__rec/_3C y) (h4/arithmetic/_2A x z))
% Assm [h4s_arithmetics_EVENu_u_MOD2]: !x. h4/arithmetic/EVEN x <=> h4/arithmetic/MOD x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/num/0
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c3]: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. happ (happ h4/prim__rec/_3C h4/num/0) (h4/arithmetic/NUMERAL n) <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/NUMERAL n)) (h4/arithmetic/NUMERAL m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. happ (happ h4/prim__rec/_3C n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT2 m) <=> ~happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_numerals_numeralu_u_lteu_c0]: !n. h4/arithmetic/_3C_3D h4/arithmetic/ZERO n <=> T
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_lteu_c3]: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (happ (happ h4/prim__rec/_3C m) n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_enumeralu_u_multu_c2]: !y x. h4/arithmetic/_2A (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y) = h4/numeral/internal__mult (h4/arithmetic/BIT1 x) (h4/arithmetic/BIT1 y)
% Assm [h4s_numerals_internalu_u_multu_u_characterisationu_c0]: !n. h4/numeral/internal__mult h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm [h4s_numerals_internalu_u_multu_u_characterisationu_c2]: !n m. h4/numeral/internal__mult (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/numeral/internal__mult n m)) m)
% Assm [h4s_basicSizes_boolu_u_sizeu_u_def]: !b. h4/basicSize/bool__size b = h4/num/0
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_sizeu_u_defu_c0]: !f. h4/list/list__size f h4/list/NIL = h4/num/0
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (happ f h) (h4/list/MAP f t)
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_lists_MAPu_u_IDu_c0]: !_0. (!x. happ _0 x = x) ==> (!l. h4/list/MAP _0 l = l)
% Assm [h4s_lists_MAPu_u_MAPu_u_o]: !l g f. h4/list/MAP f (h4/list/MAP g l) = h4/list/MAP (h4/combin/o f g) l
% Assm [h4s_lists_MEMu_c0]: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm [h4s_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_ADDu_u_ASSOC]: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm [h4s_integers_intu_u_sub0]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_ADDu_u_RID]: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_integers_INTu_u_ADDu_u_RINV]: !x. h4/integer/int__add x (h4/integer/int__neg x) = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_MULu_u_LID]: !x. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_integers_INTu_u_RDISTRIB]: !z y x. h4/integer/int__mul (h4/integer/int__add x y) z = h4/integer/int__add (h4/integer/int__mul x z) (h4/integer/int__mul y z)
% Assm [h4s_integers_INTu_u_NEGu_u_ADD]: !y x. h4/integer/int__neg (h4/integer/int__add x y) = h4/integer/int__add (h4/integer/int__neg x) (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_MULu_u_LZERO]: !x. h4/integer/int__mul (h4/integer/int__of__num h4/num/0) x = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_NEGu_u_LMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm [h4s_integers_INTu_u_NEGNEG]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integers_INTu_u_NOTu_u_LT]: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm [h4s_integers_INTu_u_LTu_u_GT]: !y x. h4/integer/int__lt x y ==> ~h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_LEu_u_REFL]: !x. h4/integer/int__le x x
% Assm [h4s_integers_INTu_u_NEGu_u_LT0]: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm [h4s_integers_INTu_u_LTu_u_ADD2]: !z y x w. h4/integer/int__lt w x /\ h4/integer/int__lt y z ==> h4/integer/int__lt (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm [h4s_integers_INTu_u_NEGu_u_MINUS1]: !x. h4/integer/int__neg x = h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) x
% Assm [h4s_integers_INTu_u_LTu_u_IMPu_u_NE]: !y x. h4/integer/int__lt x y ==> ~(x = y)
% Assm [h4s_integers_INTu_u_LTu_u_SUBu_u_RADD]: !z y x. h4/integer/int__lt (h4/integer/int__sub x y) z <=> h4/integer/int__lt x (h4/integer/int__add z y)
% Assm [h4s_integers_INTu_u_LTu_u_SUBu_u_LADD]: !z y x. h4/integer/int__lt x (h4/integer/int__sub y z) <=> h4/integer/int__lt (h4/integer/int__add x z) y
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_RADD]: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm [h4s_integers_INTu_u_SUBu_u_LZERO]: !x. h4/integer/int__sub (h4/integer/int__of__num h4/num/0) x = h4/integer/int__neg x
% Assm [h4s_integers_INTu_u_EQu_u_SUBu_u_LADD]: !z y x. x = h4/integer/int__sub y z <=> h4/integer/int__add x z = y
% Assm [h4s_integers_NUMu_u_OFu_u_INT]: !n. h4/integer/Num (h4/integer/int__of__num n) = n
% Assm [h4s_integers_INTu_u_OFu_u_NUM]: !i. h4/integer/int__of__num (h4/integer/Num i) = i <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) i
% Assm [h4s_integers_INTu_u_DIVIDESu_u_1u_c0]: !x. h4/integer/int__divides (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x
% Assm [h4s_integers_INTu_u_MINu_u_LT]: !z y x. h4/integer/int__lt x (h4/integer/int__min y z) ==> h4/integer/int__lt x y /\ h4/integer/int__lt x z
% Assm [h4s_integers_INTu_u_MAXu_u_LT]: !z y x. h4/integer/int__lt (h4/integer/int__max x y) z ==> h4/integer/int__lt x z /\ h4/integer/int__lt y z
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c0]: !p. h4/integer/int__add (h4/integer/int__of__num h4/num/0) p = p
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c1]: !p. h4/integer/int__add p (h4/integer/int__of__num h4/num/0) = p
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c2]: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c5]: !n m. h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))))
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c6]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D m n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m))))
% Assm [h4s_integers_INTu_u_ADDu_u_REDUCEu_c7]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))))
% Assm [h4s_integers_INTu_u_SUBu_u_CALCULATE]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_SUBu_u_REDUCEu_c2]: !n m. h4/integer/int__sub (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__add (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)))
% Assm [h4s_integers_INTu_u_MULu_u_REDUCEu_c2]: !n m. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2A m n))
% Assm [h4s_integers_INTu_u_MULu_u_REDUCEu_c3]: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/_2A m n)))
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c0]: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c2]: h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num h4/num/0) <=> F
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c5]: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c6]: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c11]: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_integers_INTu_u_EQu_u_REDUCEu_c1]: !n. h4/integer/int__of__num h4/num/0 = h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) <=> F
% Assm [h4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_left]: !z y x. h4/integer/int__lt x (h4/integer/int__add y z) <=> h4/integer/int__lt (h4/integer/int__add x (h4/integer/int__neg y)) z
% Assm [h4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_right]: !z y x. h4/integer/int__lt (h4/integer/int__add x y) z <=> h4/integer/int__lt y (h4/integer/int__add z (h4/integer/int__neg x))
% Assm [h4s_intu_u_ariths_equ_u_moveu_u_leftu_u_left]: !z y x. x = h4/integer/int__add y z <=> h4/integer/int__add x (h4/integer/int__neg y) = z
% Assm [h4s_intu_u_ariths_equ_u_moveu_u_leftu_u_right]: !z y x. h4/integer/int__add x y = z <=> y = h4/integer/int__add z (h4/integer/int__neg x)
% Assm [h4s_intu_u_ariths_lcmu_u_eliminate]: !c P. (?x. happ P (h4/integer/int__mul c x)) <=> (?x. happ P x /\ h4/integer/int__divides c x)
% Assm [h4s_intu_u_ariths_canu_u_getu_u_small]: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt (h4/integer/int__sub y (h4/integer/int__mul c d)) x)
% Assm [h4s_intu_u_ariths_canu_u_getu_u_big]: !y x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c /\ h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_restrictedu_u_quantificationu_u_simp]: !x low high. h4/integer/int__lt low x /\ h4/integer/int__le x high <=> h4/integer/int__lt low high /\ (x = high \/ h4/integer/int__lt low x /\ h4/integer/int__le x (h4/integer/int__sub high (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_intu_u_ariths_topu_u_andu_u_lessers]: !x0 d P. (!x. happ P x ==> happ P (h4/integer/int__sub x d)) /\ happ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> happ P (h4/integer/int__sub x0 (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_botu_u_andu_u_greaters]: !x0 d P. (!x. happ P x ==> happ P (h4/integer/int__add x d)) /\ happ P x0 ==> (!c. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) c ==> happ P (h4/integer/int__add x0 (h4/integer/int__mul c d)))
% Assm [h4s_intu_u_ariths_inu_u_additiveu_u_range]: !x low d. h4/integer/int__lt low x /\ h4/integer/int__le x (h4/integer/int__add low d) <=> (?j. x = h4/integer/int__add low j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm [h4s_intu_u_ariths_inu_u_subtractiveu_u_range]: !x high d. h4/integer/int__le (h4/integer/int__sub high d) x /\ h4/integer/int__lt x high <=> (?j. x = h4/integer/int__sub high j /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) j /\ h4/integer/int__le j d)
% Assm [h4s_intu_u_ariths_subtractu_u_tou_u_small]: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__sub x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__sub x (h4/integer/int__mul k d)) d)
% Assm [h4s_intu_u_ariths_addu_u_tou_u_great]: !x d. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) d ==> (?k. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__add x (h4/integer/int__mul k d)) /\ h4/integer/int__le (h4/integer/int__add x (h4/integer/int__mul k d)) d)
% Assm [h4s_intu_u_ariths_INTu_u_NUMu_u_FORALL]: !P. (!n. happ P (h4/integer/int__of__num n)) <=> (!x. h4/integer/int__le (h4/integer/int__of__num h4/num/0) x ==> happ P x)
% Assm [h4s_intu_u_bitwises_intu_u_notu_u_def]: !i. happ h4/int__bitwise/int__not i = h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__of__num h4/num/0) i) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_intu_u_bitwises_bitsu_u_ofu_u_numu_u_primitiveu_u_def]: !_2. (!bits__of__num n. ?v. (v <=> n = h4/num/0) /\ happ (happ _2 bits__of__num) n = h4/combin/I (h4/bool/COND v h4/list/NIL (h4/list/CONS (h4/arithmetic/ODD n) (happ bits__of__num (h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))) ==> (!_1. (!bits__of__num. happ _1 bits__of__num = happ _2 bits__of__num) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!n. ~(n = h4/num/0) ==> happ (happ R (h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) n)) ==> h4/int__bitwise/bits__of__num = h4/relation/WFREC (h4/min/_40 _0) _1))
% Assm [h4s_intu_u_bitwises_bitsu_u_ofu_u_numu_u_def]: !n. ?v. (v <=> n = h4/num/0) /\ happ h4/int__bitwise/bits__of__num n = h4/bool/COND v h4/list/NIL (h4/list/CONS (h4/arithmetic/ODD n) (happ h4/int__bitwise/bits__of__num (h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))
% Assm [h4s_intu_u_bitwises_bitsu_u_ofu_u_intu_u_def]: !i. h4/int__bitwise/bits__of__int i = h4/bool/COND (h4/integer/int__lt i (h4/integer/int__of__num h4/num/0)) (h4/pair/_2C (h4/list/MAP $not (happ h4/int__bitwise/bits__of__num (h4/integer/Num (happ h4/int__bitwise/int__not i)))) T) (h4/pair/_2C (happ h4/int__bitwise/bits__of__num (h4/integer/Num i)) F)
% Assm [h4s_intu_u_bitwises_numu_u_ofu_u_bitsu_u_primitiveu_u_def]: !_4. (!v num__of__bits bs. happ (happ (happ _4 v) num__of__bits) bs = h4/bool/COND v (h4/combin/I (h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (happ num__of__bits bs)))) (h4/combin/I (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (happ num__of__bits bs)))) ==> (!_3. (!num__of__bits v. happ (happ _3 num__of__bits) v = happ (happ _4 v) num__of__bits) ==> (!_2. (!num__of__bits a. happ (happ _2 num__of__bits) a = h4/list/list__CASE a (h4/combin/I h4/num/0) (happ _3 num__of__bits)) ==> (!_1. (!num__of__bits. happ _1 num__of__bits = happ _2 num__of__bits) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!bs. happ (happ R bs) (h4/list/CONS F bs)) /\ (!bs. happ (happ R bs) (h4/list/CONS T bs))) ==> h4/int__bitwise/num__of__bits = h4/relation/WFREC (h4/min/_40 _0) _1))))
% Assm [h4s_intu_u_bitwises_intu_u_ofu_u_bitsu_u_def]: !rest bs. h4/int__bitwise/int__of__bits (h4/pair/_2C bs rest) = h4/bool/COND rest (happ h4/int__bitwise/int__not (h4/integer/int__of__num (happ h4/int__bitwise/num__of__bits (h4/list/MAP $not bs)))) (h4/integer/int__of__num (happ h4/int__bitwise/num__of__bits bs))
% Assm [h4s_intu_u_bitwises_bitsu_u_bitwiseu_u_tupledu_u_primitiveu_u_def]: !_18. (!_13 b1_27 b2 bits__bitwise__tupled f r1 bs2 r2 bs1_27. happ (happ (happ (happ (happ (happ (happ (happ (happ _18 _13) b1_27) b2) bits__bitwise__tupled) f) r1) bs2) r2) bs1_27 = h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ (happ _13 f) b1_27) b2)) (happ bits__bitwise__tupled (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1_27 r1) (h4/pair/_2C bs2 r2)))))) ==> (!_17. (!_13 b2 bits__bitwise__tupled f r1 bs2 r2 b1_27. happ (happ (happ (happ (happ (happ (happ (happ _17 _13) b2) bits__bitwise__tupled) f) r1) bs2) r2) b1_27 = happ (happ (happ (happ (happ (happ (happ (happ _18 _13) b1_27) b2) bits__bitwise__tupled) f) r1) bs2) r2) ==> (!_16. (!v4 _13 b2 bits__bitwise__tupled f r1 r2 bs2. happ (happ (happ (happ (happ (happ (happ (happ _16 v4) _13) b2) bits__bitwise__tupled) f) r1) r2) bs2 = h4/list/list__CASE v4 (h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ (happ _13 f) r1) b2)) (happ bits__bitwise__tupled (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C h4/list/NIL r1) (h4/pair/_2C bs2 r2)))))) (happ (happ (happ (happ (happ (happ (happ _17 _13) b2) bits__bitwise__tupled) f) r1) bs2) r2)) ==> (!_15. (!v4 _13 bits__bitwise__tupled f r1 r2 b2. happ (happ (happ (happ (happ (happ (happ _15 v4) _13) bits__bitwise__tupled) f) r1) r2) b2 = happ (happ (happ (happ (happ (happ (happ _16 v4) _13) b2) bits__bitwise__tupled) f) r1) r2) ==> (!_14. (!f b1 r2 bs r. happ (happ (happ (happ (happ _14 f) b1) r2) bs) r = h4/pair/_2C (h4/list/CONS (happ (happ f b1) r2) bs) r) ==> (!_13. (!f b1 r2 bs. happ (happ (happ (happ _13 f) b1) r2) bs = happ (happ (happ (happ _14 f) b1) r2) bs) ==> (!_12. (!b1 bits__bitwise__tupled f r1 r2 bs1. happ (happ (happ (happ (happ (happ _12 b1) bits__bitwise__tupled) f) r1) r2) bs1 = h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ (happ _13 f) b1) r2)) (happ bits__bitwise__tupled (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1 r1) (h4/pair/_2C h4/list/NIL r2)))))) ==> (!_11. (!bits__bitwise__tupled f r1 r2 b1. happ (happ (happ (happ (happ _11 bits__bitwise__tupled) f) r1) r2) b1 = happ (happ (happ (happ (happ _12 b1) bits__bitwise__tupled) f) r1) r2) ==> (!_10. (!v6 v4 bits__bitwise__tupled f r1 r2. happ (happ (happ (happ (happ (happ _10 v6) v4) bits__bitwise__tupled) f) r1) r2 = h4/list/list__CASE v6 (h4/list/list__CASE v4 (h4/combin/I (h4/pair/_2C h4/list/NIL (happ (happ f r1) r2))) (happ (happ (happ (happ _11 bits__bitwise__tupled) f) r1) r2)) (happ (happ (happ (happ (happ (happ _15 v4) _13) bits__bitwise__tupled) f) r1) r2)) ==> (!_9. (!v4 bits__bitwise__tupled f r1 v6. happ (happ (happ (happ (happ _9 v4) bits__bitwise__tupled) f) r1) v6 = happ (happ (happ (happ (happ _10 v6) v4) bits__bitwise__tupled) f) r1) ==> (!_8. (!v3 v4 bits__bitwise__tupled f r1. happ (happ (happ (happ (happ _8 v3) v4) bits__bitwise__tupled) f) r1 = h4/pair/pair__CASE v3 (happ (happ (happ (happ _9 v4) bits__bitwise__tupled) f) r1)) ==> (!_7. (!v3 bits__bitwise__tupled f v4. happ (happ (happ (happ _7 v3) bits__bitwise__tupled) f) v4 = happ (happ (happ (happ _8 v3) v4) bits__bitwise__tupled) f) ==> (!_6. (!v2 bits__bitwise__tupled f v3. happ (happ (happ (happ _6 v2) bits__bitwise__tupled) f) v3 = h4/pair/pair__CASE v2 (happ (happ (happ _7 v3) bits__bitwise__tupled) f)) ==> (!_5. (!bits__bitwise__tupled f v2. happ (happ (happ _5 bits__bitwise__tupled) f) v2 = happ (happ (happ _6 v2) bits__bitwise__tupled) f) ==> (!_4. (!bits__bitwise__tupled f v1. happ (happ (happ _4 bits__bitwise__tupled) f) v1 = h4/pair/pair__CASE v1 (happ (happ _5 bits__bitwise__tupled) f)) ==> (!_3. (!bits__bitwise__tupled f. happ (happ _3 bits__bitwise__tupled) f = happ (happ _4 bits__bitwise__tupled) f) ==> (!_2. (!bits__bitwise__tupled a. happ (happ _2 bits__bitwise__tupled) a = h4/pair/pair__CASE a (happ _3 bits__bitwise__tupled)) ==> (!_1. (!bits__bitwise__tupled. happ _1 bits__bitwise__tupled = happ _2 bits__bitwise__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!b2 r2 bs2 r1 f. happ (happ R (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C h4/list/NIL r1) (h4/pair/_2C bs2 r2)))) (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C h4/list/NIL r1) (h4/pair/_2C (h4/list/CONS b2 bs2) r2)))) /\ (!b1 r2 r1 bs1 f. happ (happ R (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1 r1) (h4/pair/_2C h4/list/NIL r2)))) (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C (h4/list/CONS b1 bs1) r1) (h4/pair/_2C h4/list/NIL r2)))) /\ (!b2 b1 r2 bs2 r1 bs1 f. happ (happ R (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C bs1 r1) (h4/pair/_2C bs2 r2)))) (h4/pair/_2C f (h4/pair/_2C (h4/pair/_2C (h4/list/CONS b1 bs1) r1) (h4/pair/_2C (h4/list/CONS b2 bs2) r2))))) ==> h4/int__bitwise/bits__bitwise__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))))))))
% Assm [h4s_intu_u_bitwises_bitsu_u_bitwiseu_u_curriedu_u_def]: !x2 x1 x. h4/int__bitwise/bits__bitwise x x1 x2 = happ h4/int__bitwise/bits__bitwise__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_intu_u_bitwises_intu_u_bitwiseu_u_def]: !j i f. happ (h4/int__bitwise/int__bitwise f i) j = h4/int__bitwise/int__of__bits (h4/int__bitwise/bits__bitwise f (h4/int__bitwise/bits__of__int i) (h4/int__bitwise/bits__of__int j))
% Goal: !_1. (!y. happ _1 y <=> ~y) ==> (!_0. (!x. happ _0 x = _1) ==> h4/int__bitwise/int__not = h4/int__bitwise/int__bitwise _0 (h4/integer/int__of__num h4/num/0))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q79195,TV_Q79191]: ![V_f, V_g]: (![V_x]: s(TV_Q79191,happ(s(t_fun(TV_Q79195,TV_Q79191),V_f),s(TV_Q79195,V_x))) = s(TV_Q79191,happ(s(t_fun(TV_Q79195,TV_Q79191),V_g),s(TV_Q79195,V_x))) => s(t_fun(TV_Q79195,TV_Q79191),V_f) = s(t_fun(TV_Q79195,TV_Q79191),V_g))).
fof(ah4s_bools_LETu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_x))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_CONDu_u_RATOR, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_g, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_bools_cond(s(t_bool,V_b),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_x)))))).
fof(ah4s_bools_CONDu_u_RAND, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27a,V_x),s(TV_u_27a,V_y))))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))))).
fof(ah4s_bools_CONDu_u_EXPAND, axiom, ![V_t2, V_t1, V_b]: (p(s(t_bool,h4s_bools_cond(s(t_bool,V_b),s(t_bool,V_t1),s(t_bool,V_t2)))) <=> ((~ (p(s(t_bool,V_b))) | p(s(t_bool,V_t1))) & (p(s(t_bool,V_b)) | p(s(t_bool,V_t2)))))).
fof(ah4s_bools_LETu_u_CONG, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f, V_N, V_M]: ((s(TV_u_27a,V_M) = s(TV_u_27a,V_N) & ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_N) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_x))))) => s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_M))) = s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_N))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_markers_ACu_u_DEF, axiom, ![V_b2, V_b1]: (p(s(t_bool,h4s_markers_ac(s(t_bool,V_b1),s(t_bool,V_b2)))) <=> (p(s(t_bool,V_b1)) & p(s(t_bool,V_b2))))).
fof(ah4s_combins_ou_u_DEF, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x)))))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_combins_k(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_NOTu_u_LESSu_u_0, axiom, ![V_n]: ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_MULTu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_MULTu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_COMPLETEu_u_INDUCTION, axiom, ![V_P]: (![V_n]: (![V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_m))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ODDu_u_EVEN, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n)))) <=> ~ (p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_LTu_u_MULTu_u_CANCELu_u_LBAREu_c0, axiom, ![V_n, V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_m)))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_arithmetics_DIVISION, axiom, ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_n)))) => ![V_k]: (s(t_h4s_nums_num,V_k) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_arithmetics_DIVu_u_UNIQUE, axiom, ![V_q, V_n, V_k]: (?[V_r]: (s(t_h4s_nums_num,V_k) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_q),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_r))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,V_n))))) => s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_q))).
fof(ah4s_arithmetics_DIVu_u_LESS, axiom, ![V_n, V_d]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_d))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_d))))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_MODu_u_LESS, axiom, ![V_n, V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_DIVu_u_LTu_u_X, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_z)))) => s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_y),s(t_h4s_nums_num,V_z))))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_z))))))).
fof(ah4s_arithmetics_EVENu_u_MOD2, axiom, ![V_x]: (p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,V_x)))) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c3, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_addu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m)))))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_lteu_c0, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_lteu_c3, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_enumeralu_u_multu_c2, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_y))))) = s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numerals_internalu_u_multu_u_characterisationu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_internalu_u_multu_u_characterisationu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_basicSizes_boolu_u_sizeu_u_def, axiom, ![V_b]: s(t_h4s_nums_num,h4s_basicsizes_boolu_u_size(s(t_bool,V_b))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_lists_listu_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_lists_MAPu_u_IDu_c0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_uu_0),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x) => ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27a),V_uu_0),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l))).
fof(ah4s_lists_MAPu_u_MAPu_u_o, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_l, V_g, V_f]: s(t_h4s_lists_list(TV_u_27c),h4s_lists_map(s(t_fun(TV_u_27b,TV_u_27c),V_f),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27c),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_MEMu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(t_bool,f)).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
fof(ah4s_integers_INTu_u_ADDu_u_COMM, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_intu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_ADDu_u_RID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_RINV, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_RDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_NEGu_u_ADD, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_MULu_u_LZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_NEGNEG, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_NOTu_u_LT, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_LTu_u_GT, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) => ~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_integers_INTu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_x))))).
fof(ah4s_integers_INTu_u_NEGu_u_LT0, axiom, ![V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_ADD2, axiom, ![V_z, V_y, V_x, V_w]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))))).
fof(ah4s_integers_INTu_u_NEGu_u_MINUS1, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_IMPu_u_NE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) => ~ (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LTu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_LTu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_SUBu_u_LZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_EQu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))) <=> s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))) = s(t_h4s_integers_int,V_y))).
fof(ah4s_integers_NUMu_u_OFu_u_INT, axiom, ![V_n]: s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_integers_INTu_u_OFu_u_NUM, axiom, ![V_i]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_i))))) = s(t_h4s_integers_int,V_i) <=> p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i)))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_1u_c0, axiom, ![V_x]: p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_integers_int,V_x))))).
fof(ah4s_integers_INTu_u_MINu_u_LT, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_min(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))))) => (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))))))).
fof(ah4s_integers_INTu_u_MAXu_u_LT, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_max(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))) => (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c0, axiom, ![V_p]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_p))) = s(t_h4s_integers_int,V_p)).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c1, axiom, ![V_p]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_p)).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c2, axiom, s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c5, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c6, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))))))).
fof(ah4s_integers_INTu_u_ADDu_u_REDUCEu_c7, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))))))).
fof(ah4s_integers_INTu_u_SUBu_u_CALCULATE, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_SUBu_u_REDUCEu_c2, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_integers_INTu_u_MULu_u_REDUCEu_c2, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_integers_INTu_u_MULu_u_REDUCEu_c3, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c0, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c2, axiom, s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c5, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c6, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c11, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_integers_INTu_u_EQu_u_REDUCEu_c1, axiom, ![V_n]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) <=> p(s(t_bool,f)))).
fof(ah4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_left, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_right, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))))))).
fof(ah4s_intu_u_ariths_equ_u_moveu_u_leftu_u_left, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))) <=> s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,V_z))).
fof(ah4s_intu_u_ariths_equ_u_moveu_u_leftu_u_right, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,V_z) <=> s(t_h4s_integers_int,V_y) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))))).
fof(ah4s_intu_u_ariths_lcmu_u_eliminate, axiom, ![V_c, V_P]: (?[V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_x)))))) <=> ?[V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_intu_u_ariths_canu_u_getu_u_small, axiom, ![V_y, V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_intu_u_ariths_canu_u_getu_u_big, axiom, ![V_y, V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_restrictedu_u_quantificationu_u_simp, axiom, ![V_x, V_low, V_high]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_high))))) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_high)))) & (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_high) | (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))).
fof(ah4s_intu_u_ariths_topu_u_andu_u_lessers, axiom, ![V_x0, V_d, V_P]: ((![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_d))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x0))))) => ![V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x0),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_botu_u_andu_u_greaters, axiom, ![V_x0, V_d, V_P]: ((![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_d))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x0))))) => ![V_c]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_c)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x0),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))))))))).
fof(ah4s_intu_u_ariths_inu_u_additiveu_u_range, axiom, ![V_x, V_low, V_d]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_d))))))) <=> ?[V_j]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_low),s(t_h4s_integers_int,V_j))) & (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_j)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_d)))))))).
fof(ah4s_intu_u_ariths_inu_u_subtractiveu_u_range, axiom, ![V_x, V_high, V_d]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,V_d))),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_high))))) <=> ?[V_j]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_high),s(t_h4s_integers_int,V_j))) & (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_j)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_d)))))))).
fof(ah4s_intu_u_ariths_subtractu_u_tou_u_small, axiom, ![V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_k]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d)))))))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d))))),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_intu_u_ariths_addu_u_tou_u_great, axiom, ![V_x, V_d]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_d)))) => ?[V_k]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d)))))))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_d))))),s(t_h4s_integers_int,V_d))))))).
fof(ah4s_intu_u_ariths_INTu_u_NUMu_u_FORALL, axiom, ![V_P]: (![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n)))))) <=> ![V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x)))) => p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_intu_u_bitwises_intu_u_notu_u_def, axiom, ![V_i]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_intu_u_bitwises_intu_u_not),s(t_h4s_integers_int,V_i))) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_intu_u_bitwises_bitsu_u_ofu_u_numu_u_primitiveu_u_def, axiom, ![V_uu_2]: (![V_bitsu_u_ofu_u_num, V_n]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),V_uu_2),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),V_bitsu_u_ofu_u_num))),s(t_h4s_nums_num,V_n))) = s(t_h4s_lists_list(t_bool),h4s_combins_i(s(t_h4s_lists_list(t_bool),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_bool),h4s_lists_nil),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),V_bitsu_u_ofu_u_num),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))) => ![V_uu_1]: (![V_bitsu_u_ofu_u_num]: s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),V_bitsu_u_ofu_u_num))) = s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),V_uu_2),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),V_bitsu_u_ofu_u_num))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R)))) & ![V_n]: (~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,V_n))))))) => s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_intu_u_bitwises_bitsu_u_ofu_u_num) = s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_relations_wfrec(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),V_uu_1))))))).
fof(ah4s_intu_u_bitwises_bitsu_u_ofu_u_numu_u_def, axiom, ![V_n]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_intu_u_bitwises_bitsu_u_ofu_u_num),s(t_h4s_nums_num,V_n))) = s(t_h4s_lists_list(t_bool),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_bool),h4s_lists_nil),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_intu_u_bitwises_bitsu_u_ofu_u_num),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))).
fof(ah4s_intu_u_bitwises_bitsu_u_ofu_u_intu_u_def, axiom, ![V_i]: s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_intu_u_bitwises_bitsu_u_ofu_u_int(s(t_h4s_integers_int,V_i))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_pairs_u_2c(s(t_h4s_lists_list(t_bool),h4s_lists_map(s(t_fun(t_bool,t_bool),d_not),s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_intu_u_bitwises_bitsu_u_ofu_u_num),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_intu_u_bitwises_intu_u_not),s(t_h4s_integers_int,V_i))))))))),s(t_bool,t))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_pairs_u_2c(s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_intu_u_bitwises_bitsu_u_ofu_u_num),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,V_i))))),s(t_bool,f)))))).
fof(ah4s_intu_u_bitwises_numu_u_ofu_u_bitsu_u_primitiveu_u_def, axiom, ![V_uu_4]: (![V_v, V_numu_u_ofu_u_bits, V_bs]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num))),V_uu_4),s(t_bool,V_v))),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))),s(t_h4s_lists_list(t_bool),V_bs))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits),s(t_h4s_lists_list(t_bool),V_bs))))))))),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits),s(t_h4s_lists_list(t_bool),V_bs))))))))) => ![V_uu_3]: (![V_numu_u_ofu_u_bits, V_v]: s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),happ(s(t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num))),V_uu_3),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))),s(t_bool,V_v))) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num))),V_uu_4),s(t_bool,V_v))),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))) => ![V_uu_2]: (![V_numu_u_ofu_u_bits, V_a]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),V_uu_2),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))),s(t_h4s_lists_list(t_bool),V_a))) = s(t_h4s_nums_num,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_bool),V_a),s(t_h4s_nums_num,h4s_combins_i(s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num))),V_uu_3),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))))) => ![V_uu_1]: (![V_numu_u_ofu_u_bits]: s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),V_uu_1),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),V_uu_2),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),V_numu_u_ofu_u_bits))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_R)))) & (![V_bs]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_R),s(t_h4s_lists_list(t_bool),V_bs))),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,f),s(t_h4s_lists_list(t_bool),V_bs)))))) & ![V_bs]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_R),s(t_h4s_lists_list(t_bool),V_bs))),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,t),s(t_h4s_lists_list(t_bool),V_bs))))))))) => s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),h4s_intu_u_bitwises_numu_u_ofu_u_bits) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),h4s_relations_wfrec(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num)),V_uu_1))))))))).
fof(ah4s_intu_u_bitwises_intu_u_ofu_u_bitsu_u_def, axiom, ![V_rest, V_bs]: s(t_h4s_integers_int,h4s_intu_u_bitwises_intu_u_ofu_u_bits(s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_pairs_u_2c(s(t_h4s_lists_list(t_bool),V_bs),s(t_bool,V_rest))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,V_rest),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_intu_u_bitwises_intu_u_not),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),h4s_intu_u_bitwises_numu_u_ofu_u_bits),s(t_h4s_lists_list(t_bool),h4s_lists_map(s(t_fun(t_bool,t_bool),d_not),s(t_h4s_lists_list(t_bool),V_bs))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_nums_num),h4s_intu_u_bitwises_numu_u_ofu_u_bits),s(t_h4s_lists_list(t_bool),V_bs)))))))).
fof(ah4s_intu_u_bitwises_bitsu_u_bitwiseu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_18]: (![V_uu_13, V_b1u_27, V_b2, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_bs2, V_r2, V_bs1u_27]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))))),V_uu_18),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(TV_u_27b,V_b1u_27))),s(TV_u_27c,V_b2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(t_h4s_lists_list(TV_u_27c),V_bs2))),s(TV_u_27c,V_r2))),s(t_h4s_lists_list(TV_u_27b),V_bs1u_27))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_combins_i(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_b1u_27))),s(TV_u_27c,V_b2))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_bs1u_27),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),V_bs2),s(TV_u_27c,V_r2))))))))))))) => ![V_uu_17]: (![V_uu_13, V_b2, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_bs2, V_r2, V_b1u_27]: s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))))),V_uu_17),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(TV_u_27c,V_b2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(t_h4s_lists_list(TV_u_27c),V_bs2))),s(TV_u_27c,V_r2))),s(TV_u_27b,V_b1u_27))) = s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))))),V_uu_18),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(TV_u_27b,V_b1u_27))),s(TV_u_27c,V_b2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(t_h4s_lists_list(TV_u_27c),V_bs2))),s(TV_u_27c,V_r2))) => ![V_uu_16]: (![V_v4, V_uu_13, V_b2, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_r2, V_bs2]: 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= s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27b),V_v4),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_combins_i(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_b2))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),V_bs2),s(TV_u_27c,V_r2))))))))))))),s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))))),V_uu_17),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(TV_u_27c,V_b2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(t_h4s_lists_list(TV_u_27c),V_bs2))),s(TV_u_27c,V_r2))))) => ![V_uu_15]: (![V_v4, V_uu_13, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_r2, V_b2]: s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),V_uu_15),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))),s(TV_u_27c,V_b2))) = s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),V_uu_16),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(TV_u_27c,V_b2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))) => ![V_uu_14]: (![V_f, V_b1, V_r2, V_bs, V_r]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_14),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_b1))),s(TV_u_27c,V_r2))),s(t_h4s_lists_list(TV_u_27a),V_bs))),s(TV_u_27a,V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_b1))),s(TV_u_27c,V_r2))),s(t_h4s_lists_list(TV_u_27a),V_bs))),s(TV_u_27a,V_r))) => ![V_uu_13]: (![V_f, V_b1, V_r2, V_bs]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_b1))),s(TV_u_27c,V_r2))),s(t_h4s_lists_list(TV_u_27a),V_bs))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_14),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_b1))),s(TV_u_27c,V_r2))),s(t_h4s_lists_list(TV_u_27a),V_bs))) => ![V_uu_12]: (![V_b1, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_r2, V_bs1]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_12),s(TV_u_27b,V_b1))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))),s(t_h4s_lists_list(TV_u_27b),V_bs1))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_combins_i(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_b1))),s(TV_u_27c,V_r2))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_bs1),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),h4s_lists_nil),s(TV_u_27c,V_r2))))))))))))) => ![V_uu_11]: (![V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_r2, V_b1]: s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))),s(TV_u_27b,V_b1))) = s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_12),s(TV_u_27b,V_b1))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))) => ![V_uu_10]: (![V_v6, V_v4, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_r2]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_10),s(t_h4s_lists_list(TV_u_27c),V_v6))),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27c),V_v6),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27b),V_v4),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_combins_i(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))))))),s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))))),s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),happ(s(t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))))),V_uu_15),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_13))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(TV_u_27c,V_r2))))) => ![V_uu_9]: (![V_v4, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1, V_v6]: s(t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_9),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))),s(t_h4s_lists_list(TV_u_27c),V_v6))) = s(t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_10),s(t_h4s_lists_list(TV_u_27c),V_v6))),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))) => ![V_uu_8]: (![V_v3, V_v4, V_bitsu_u_bitwiseu_u_tupled, V_f, V_r1]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_v3))),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_v3),s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27c,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))))),V_uu_9),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_r1))))) => ![V_uu_7]: (![V_v3, V_bitsu_u_bitwiseu_u_tupled, V_f, V_v4]: s(t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_7),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_v3))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_v4))) = s(t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_v3))),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) => ![V_uu_6]: (![V_v2, V_bitsu_u_bitwiseu_u_tupled, V_f, V_v3]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_v3))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),V_v2),s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))))),V_uu_7),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_v3))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))))) => ![V_uu_5]: (![V_bitsu_u_bitwiseu_u_tupled, V_f, V_v2]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),V_v2))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) => ![V_uu_4]: (![V_bitsu_u_bitwiseu_u_tupled, V_f, V_v1]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),V_v1))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),V_v1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))))) => ![V_uu_3]: (![V_bitsu_u_bitwiseu_u_tupled, V_f]: s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) => ![V_uu_2]: (![V_bitsu_u_bitwiseu_u_tupled, V_a]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),V_a))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),V_a),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))))) => ![V_uu_1]: (![V_bitsu_u_bitwiseu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),V_bitsu_u_bitwiseu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),V_R)))) & (![V_b2, V_r2, V_bs2, V_r1, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),V_bs2),s(TV_u_27c,V_r2))))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),h4s_lists_cons(s(TV_u_27c,V_b2),s(t_h4s_lists_list(TV_u_27c),V_bs2))),s(TV_u_27c,V_r2)))))))))) & (![V_b1, V_r2, V_r1, V_bs1, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_bs1),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),h4s_lists_nil),s(TV_u_27c,V_r2))))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,V_b1),s(t_h4s_lists_list(TV_u_27b),V_bs1))),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),h4s_lists_nil),s(TV_u_27c,V_r2)))))))))) & ![V_b2, V_b1, V_r2, V_bs2, V_r1, V_bs1, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_bs1),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),V_bs2),s(TV_u_27c,V_r2))))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,V_b1),s(t_h4s_lists_list(TV_u_27b),V_bs1))),s(TV_u_27b,V_r1))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),h4s_lists_cons(s(TV_u_27c,V_b2),s(t_h4s_lists_list(TV_u_27c),V_bs2))),s(TV_u_27c,V_r2)))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),h4s_intu_u_bitwises_bitsu_u_bitwiseu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a))),V_uu_1))))))))))))))))))))))).
fof(ah4s_intu_u_bitwises_bitsu_u_bitwiseu_u_curriedu_u_def, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_x2, V_x1, V_x]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_intu_u_bitwises_bitsu_u_bitwise(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_x),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),V_x1),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_x2))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),TV_u_27a)),h4s_intu_u_bitwises_bitsu_u_bitwiseu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_x),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27b),V_x1),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27c),V_x2)))))))).
fof(ah4s_intu_u_bitwises_intu_u_bitwiseu_u_def, axiom, ![V_j, V_i, V_f]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_intu_u_bitwises_intu_u_bitwise(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_j))) = s(t_h4s_integers_int,h4s_intu_u_bitwises_intu_u_ofu_u_bits(s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_intu_u_bitwises_bitsu_u_bitwise(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_intu_u_bitwises_bitsu_u_ofu_u_int(s(t_h4s_integers_int,V_i))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_bool),h4s_intu_u_bitwises_bitsu_u_ofu_u_int(s(t_h4s_integers_int,V_j)))))))).
fof(ch4s_intu_u_bitwises_intu_u_not0, conjecture, ![V_uu_1]: (![V_y]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),V_uu_1),s(t_bool,V_y)))) <=> ~ (p(s(t_bool,V_y)))) => ![V_uu_0]: (![V_x]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_0),s(t_bool,V_x))) = s(t_fun(t_bool,t_bool),V_uu_1) => s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_intu_u_bitwises_intu_u_not) = s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_intu_u_bitwises_intu_u_bitwise(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_0),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))).
